Randomly branched bisphenol A polycarbonates. I. Molecular weight distribution modeling,interfacial synthesis,and characterization

Randomly branched bisphenol A polycarbonates (PCs) were prepared by interfacial polymerization methods to explore the limits of gel‐free compositions available by the adjustment of various composition and process variables. A molecular weight distribution (MWD) model was devised to predict the MWD, G, and weight‐average molecular weight per arm (M_w /arm) values based on the composition variables. The amounts of the monomer, branching agent, and chain terminator must be adjusted such that the weight‐average functionality of the phenolic monomers (F_OH ) was less than 2 to preclude gel formation in both the long‐ and short‐chain branched (SCB) PCs. Several series of SCB and long‐chain branched PCs were prepared, and those lacking gels showed molecular weights measured by gel permeation chromatography–UV and gel permeation chromatography–LS consistent with model calculations. In SCB PCs, the minimum M_w /arm that could be realized without gel formation depended on both composition (molecular weight, terminator type) and process (terminator addition point, coupling catalyst) variables. The minimum M_w /arm achieved in the low molecular weight series studied ranged from ∼3300 to ∼1000. The use of long chain alkyl phenol terminators gave branched PCs with lower glass‐transition temperatures but a higher gel‐free minimum M_w /arm. SCB PCs where M_w /arm was less than ∼M_c spontaneously cracked after compression molding, a result attributed to their lack of polymer chain entanglements. © 2000 John Wiley & Sons, Inc. J Polym Sci A: Polym Chem 38: 560–570, 2000     

Simple and effective one‐pot synthesis of (meth)acrylic block copolymers through atom transfer radical polymerization

The synthesis of di‐ and triblock copolymers using atom transfer radical polymerization (ATRP) of n‐butyl acrylate (BA) and methyl methacrylate (MMA) is reported. In particular, synthetic procedures that allow for an easy and convenient synthesis of such block copolymers were developed by using CuBr and CuCl salts complexed with linear amines. Polymerizations were successfully conducted where the monomers were added to the reactor in a sequential manner. Poor cross‐propagation between poly(n‐butyl acrylate) (PBA) macroinitiators and MMA was minimized, and therefore control of molecular weights and distributions was realized, by using halogen exchange—a technique involving the addition of CuCl to the MMA during the chain extension of the PBA macroinitiator. High molecular weight (M_n ∼ 90,000) and low polydispersity (M_w /M_n < 1.35) ABA triblock copolymers were also prepared and their structure and properties in bulk have been preliminary characterized indicating the potential of ATRP for the production of all‐acrylic thermoplastic elastomers. © 2000 John Wiley & Sons, Inc. J Polym Sci A: Polym Chem 38: 2023–2031, 2000     

Four‐terminal reducibility and projective‐planar wye‐delta‐wye‐reducible graphs

A graph is YΔY‐reducible if it can be reduced to a vertex by a sequence of series‐parallel reductions and YΔY‐transformations. Terminals are distinguished vertices, that cannot be deleted by reductions and transformations. In this article, we show that four‐terminal planar graphs are YΔY‐reducible when at least three of the vertices lie on the same face. Using this result, we characterize YΔY‐reducible projective‐planar graphs. We also consider terminals in projective‐planar graphs, and establish that graphs of crossing‐number one are YΔY‐reducible. © 2000 John Wiley & Sons, Inc. J Graph Theory 33: 83–93, 2000